![]() This is because the imaging is conducted in image space. RDI neither restricts the sample plane nor requires a high dynamic range or sensitivity for a detector. This configuration enables a significantly simpler realization than similar modalities 37. For diffusive samples, the Fourier spectrum satisfies the tight support edge condition of Fienup’s hybrid input–output (HIO) algorithm 29 even for an elementary Fourier mask. Hence, we termed it as “reciprocal diffractive imaging (RDI).” In RDI, a single mask placed in the Fourier plane filters the sample beam, and the intensity distribution is measured in the image plane. The principle and optical setup are reciprocal to those of CDI. This study circumvents these drawbacks of CDI by limiting the field to a known support in the Fourier plane. For example, a loosened support condition was presented for imaging of separated objects 35 however, this method can still target only certain types of samples corresponding to separated objects. Recently, efforts have been made to alleviate the strict support condition of CDI 35, 36. The deviation in the sample spectrum from the support can cause significant errors in the reconstructed field. In addition, imposing a sample support limits the types of samples that can be imaged and requires prior knowledge of the sample 33, 34. It may miss low spatial frequency information in the vicinity of zero spatial frequency 30, 31, 32. The Fourier spectrum has strong power at low frequencies. CDI measures the intensity in the Fourier plane (or the far-field diffraction plane) while limiting the optical field to geometric support in the sample plane 29. Although single-shot FPM techniques 24, 25 have been proposed, these methods limit the field of view or spatial resolution and need an additional module, such as a lens array, which makes the optical setup unwieldy.Ĭoherent diffractive imaging (CDI) is a single-shot non-interferometric method that is extensively utilized in X-ray imaging 26, 27, 28. This algorithm increases the data acquisition time. However, FPM requires redundant intensity images because the Fourier spectra of the different measurements need to be superimposed to reconstruct an optical field. Through a synthetic-aperture-based method, objects that we see in our daily lives can be holographically recorded in a reference-free regime. successfully retrieved the field scattered from optically rough samples using reflective FPM. Reflective FPM exploits the reflection geometry for imaging diffusive samples 20, 21, 22. It iteratively maps the Fourier transform of the acquired images in Fourier space. ![]() FPM reconstructs an optical field by measuring the intensity distributions generated from various incident angles. Fourier ptychographic microscopy (FPM) 18, 19 has emerged as a popular intensity-based holographic method. By contrast, non-interferometric or intensity-based techniques enable holographic measurements without using a reference beam and allow simpler and more stable optical setups 16, 17. However, these methods often require complex optical systems. Widely adopted holographic-field measurement methods such as off-axis 14 or phase-shifting holography 15 employ interferometry to obtain the phase information of an object. Moreover, holographic cameras can be used in conjunction with holographic displays or virtual reality technology to improve realism 12, 13. This unique capability of holographic cameras is utilized in various fields, including 3D vision systems 1, 2, 3, 4, 5, 6 and microscopic imaging of unlabeled samples 7, 8, 9, 10, 11. By contrast, a holographic camera provides volumetric information about a three-dimensional (3D) object by measuring its amplitude and phase. As the optical focus cannot be changed, information is lost owing to the blurring of the out-of-focus parts of the image. Therefore, it only shows a projected image of the intensity distribution. A conventional image sensor cannot perceive the depth of an object.
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